Simple Interest
Math MCQs

Question :    If Sandra paid $4984 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4450

Solution & Explanation

Solution

Given,

Amount (A) = $4984

Rate of Simple Interest (R) = 3%

Time (T) = 4 years

Thus, Principal (P) = ?

Method (1) Using Formula

Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given

Formula to find the Principal (P)

Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)

⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]

⇒ A = P (1 + RT)

Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given

In the given question, we need to find the Principal (P)

Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get

$4984 = P (1 + 3% × 4)

⇒ $4984 = P (1 + ³/₁₀₀ × 4)

⇒ $4984 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $4984 = P (1 + ¹²/₁₀₀)

⇒ $4984 = P (^{100 + 12}/₁₀₀)

⇒ $4984 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4984

⇒ P = ⁴⁹⁸⁴/_¹¹²/100

⇒ P = 4984 × ¹⁰⁰/₁₁₂

⇒ P = ^{4984 × 100}/₁₁₂

⇒ P = ⁴⁹⁸⁴⁰⁰/₁₁₂

⇒ P = $4450

Thus, the sum borrowed (P) = $4450 Answer

Method (1) Using Unitary Method

Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given

Calculation of the Simple Interest

Let, the principal = 100

Here, since rate of simple interest = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

Calculation of the Amount

Since, in the question, time = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 3 = 12

Thus, simple interest for 4 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 4984, then the Principal = ¹⁰⁰/₁₁₂ × 4984

= ^{100 × 4984}/₁₁₂

= ⁴⁹⁸⁴⁰⁰/₁₁₂

= 4450

Thus, Principal = $4450

Thus, the sum borrowed = $4450 Answer

Similar Questions

(1) If Margaret paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(2) Jessica had to pay $4087.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(3) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $10498 to clear the loan, then find the time period of the loan.

(4) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 8% simple interest?

(5) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 3% simple interest?

(6) How much loan did Sarah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7020 to clear it?

(7) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.

(8) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.

(9) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 7% simple interest?

(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 4 years.